Reference-Class Problems Are Real: Health-Adjusted Reference Classes and Low Bone Mineral Density

Abstract

Elselijn Kingma argues that Christopher Boorse’s biostatistical theory (the BST) does not show how the reference classes it uses are objective and naturalistic. Recently, philosophers of medicine have attempted to rebut Kingma’s concerns. I argue that these rebuttals are theoretically unconvincing, and that there are clear examples of physicians adjusting their reference classes according to their prior knowledge of health and disease. I focus on the use of age-adjusted reference classes to diagnose low bone mineral density in children. In addition to using the BST’s age, sex, and species, physicians also choose to use other factors to define reference classes, such as pubertal status, bone age, body size, and muscle mass. I show that physicians calibrate the reference classes they use according to their prior knowledge of health and disease. Reference classes are also chosen for pragmatic reasons, such as to predict fragility fractures.

I. INTRODUCTION

The reference-class problem presents a challenge to the purportedly objective and naturalistic biostatistical theory of health and disease (the BST). According to the BST, health is statistically typical functioning, and disease is atypically diminished functioning. Setting aside issues of defining and assessing biological function, the functioning of an individual is considered typical or atypical in comparison to a population: a reference class. According to the BST, reference classes are natural classes of organisms of uniform functional design, and the correct reference classes are individuals of the same species, sex, age, and perhaps race. If the correct reference classes cannot be defined objectively and naturalistically, then the BST cannot be objective and naturalistic. This in turn opens up the possibility that physicians can choose to use a variety of different reference classes according to their intuitions about who is healthy and who is diseased, for example, generating a variety of different disease concepts.

Philosophers have recently tried to dismiss the reference-class problem as misbegotten and irrelevant to medical practice (Boorse, 2014; Werkhoven, 2020). First, I provide a theoretical defense of the reference-class problem as a substantial issue. I discuss how the BST defines reference classes in terms of biological function, and biological function in terms of reference classes. I show that reference classes are those differences in biological functioning that have been deemed acceptable. Philosophers like Elselijn Kingma have argued that the BST does not make this decision objectively or naturalistically, and therefore that this decision must be made according to unarticulated value judgments. Consequently, the selection of reference classes amounts to the assertion that some differences in biological functioning are acceptable and should count as healthy and not as diseases. Because the BST asserts what it claims to demonstrate, Kingma argues that using the BST to distinguish health and disease results in a circular argument. I show that attempts to dismiss the reference-class problem actually demonstrate its seriousness.

I go on to provide examples of the reference-class problem manifesting in medical practice. Christopher Boorse (2014) has defended the BST by denying that there are any examples of physicians having to choose between different candidate concepts of disease generated by using different reference classes. I take Boorse’s objections as a challenge that should be met empirically.

The disease osteoporosis has received some attention from philosophers of medicine, especially with regard to the question of reference classes used in the definition of this disease (DeVito, 2000; Boorse, 2014). The World Health Organization (WHO) (2007) defines osteoporosis as having low bone mineral density in comparison to the average of a young adult population. Thus, the bone mineral density of elderly women is judged against that of young women. This comparison with a young reference class generates a “T-score,” which is the number of standard deviations an individual’s bone mineral density is below the young average.

However, physicians do not only use the T-score to define osteoporosis or low bone mineral density. They also use age-adjusted reference classes to define low bone mineral density in children, producing what is called a “Z-score.” I explore which factors physicians use to define reference classes when producing Z-scores, and why they use them (see Age-adjusted reference classes: the Z-score). Age and sex are important factors used to define reference classes (see Low bone density in children: age, sex, and race-adjusted reference classes). However, in addition to age and sex, Z-scores are generated by paying attention to pubertal status, body size, and muscular development (see Pubertal age, size, bone age, and height age). This counts against the BST. Even so, some physicians justify their use of these factors to define reference classes in terms of a person’s life stages and in terms of biological functioning, which is in keeping with the BST (see Functional accounts of pubertal age and body size). However, I find that the factors taken into account when defining reference classes are calibrated using knowledge of which patients are healthy and which are diseased. As critics of the BST fear, these are not just age-adjusted reference classes, they are health-adjusted reference classes (see Pragmatic solutions to continuing challenges for assessing bone mineral density). I also show how physicians calibrate reference classes to allow them to predict fragility fractures, showing that naturalistic considerations are deemed less important than pragmatic ones. Exploring how reference classes are used to generate Z-scores reveals a complex mixture of competing intuitions, some of which are in keeping with the BST, and some of which are not. Ultimately, I show that the philosophical concerns of these critics are well founded.

II. THE REFERENCE-CLASS PROBLEM

Christopher Boorse (1997) has sought to articulate a theory of health and disease that defines these concepts objectively, without the need to appeal to value judgments. Boorse argues that disease is a state in which the functional ability of at least one of an organism’s parts or processes is reduced below the levels typical for that kind of organism. Boorse’s theory therefore depends on being able to define biological functions and the reference class to which an organism belongs in an objective and value-independent way. He describes his biostatistical theory as follows:

• The reference class is a natural class of organisms of uniform functional design; specifically, an age group of a sex of a species.

• A normal function of a part or process within members of the reference class is a statistically typical contribution by it to their individual survival [or] reproduction.

• Health in a member of the reference class is normal functional ability: the readiness of each internal part to perform all its normal functions on typical occasions with at least typical efficiency.

• A disease [later, pathological condition] is a type of internal state that impairs health, that is, reduces one or more functional abilities below typical efficiency. (Boorse, 2014, 684)

Boorse has a sophisticated account of why survival and reproduction are the objective apical goals of human organisms, and therefore about why contributions to survival or reproduction are biological functions. He argues that living organisms are organized systems, and researchers can study them to discover the goals toward which they are organized (Boorse, 1976, 1977, 1997). Boorse argues that when individual organisms are studied by physiologists, they should find that the organization of these individuals is in fact oriented toward their survival and reproduction. However, his account of how reference classes can be defined objectively is less well developed. Several scholars have argued that Boorse fails to define reference classes objectively (Neander, 1983; DeVito, 2000; Cooper, 2002; Kingma, 2007). In particular, Boorse’s account appears to be a circular argument, since function is defined in terms of the reference class, and reference class is defined in terms of function.

Let us consider the lens of the human eye. Many lenses focus light onto the retina, facilitating vision. However, some people have severe cataracts, and their lenses prevent light from reaching the retina. According to Boorse, the lens ought to function by focusing light on the retina even in patients with severe cataracts, because that is what the lens typically does in other beings. Accordingly, the biological function of a lens in an individual can only be defined once the reference class of organisms to which that individual belongs is defined. However, a reference class is a “natural class of organisms of uniform functional design”—a group of organisms that function in the same way as each other. Accordingly, the reference class can only be defined once the biological function of the lens is known. So, Boorse defines function in terms of reference class, and reference class in terms of function.

Karen Neander (1983, 2017) has identified that the circularity of these definitions is a problem for Boorse’s (2002) account. Boorse (2002) responded to this objection by maintaining that knowledge of function is independent of and prior to knowledge of reference class. Reference classes correspond to groups of human beings whose parts function in the same way. As men and women function differently (e.g., with regard to their reproductive organs), Boorse allows reference classes to reflect sex differences. As human beings function differently as they age (e.g., human females go through puberty and then the menopause), Boorse (1977) allows reference classes to reflect age differences. This is why Boorse argues that reference classes are composed of individuals of the same species, sex, and age. Given this, however, it is not clear what to do about cases such as the cataracts example just discussed. People with cataracts also function differently from other human beings, so why should not they get their own reference class? Diabetics and patients with Down syndrome function differently from other human beings, so why should not they get their own reference class? (Kingma, 2007).

Kingma (2007) argues that Boorse’s appeal to the “natural class of organisms of uniform functional design” to justify the BST’s selection reference classes does not do this work. The differences in functioning that the BST deems pathological are just as natural as the functional differences it deems healthy. Cataracts exist in nature just as the menopause does. Boys, girls, men, women, people with Down syndrome, and diabetics all have equal claim to being natural kinds (Kingma, 2007).

Kingma also considers that natural may mean statistically normal. On this view, individuals who function differently from others have to be found frequently in the species in question, if they are to have their own reference class. She rejects this view because in some species there are very small numbers of individuals who function very differently from other members of that species, who nonetheless must qualify as having a reference class of their own, such as the queen bee. “[T]he queen design in bees should certainly count as a reference class if anything does. It is, however, very rarely encountered” (Kingma, 2007, 129). If, in some horrifying other world, the numbers of one of the human sexes were drastically diminished, would this mean that this sex would not qualify as a reference class, and thus be seen as diseased? Whatever Boorse has in mind when invoking a “natural class of organisms,” Kingma doubts groups of differently functioning individuals can be denied their own reference class on the basis of their prevalence.

Boorse also argues that the relevant kinds are those groups in which differences in function typically occur together. So men typically have testicles, a penis, and less mammary development, whereas women have ovaries, a womb, and more mammary development (Boorse, 1977). Uniformity, then, may be understood as the covariance of functional characteristics. “The female characters occur together, and constitute a single coherent functional design, as do the male’s” (Boorse, 1977, 558). But covariance can be cashed out in lots of different ways. Male dogs and male sheep also have a penis, testicles, and underdeveloped mammary tissue, so are these to join male human beings in a reference class? This is a trivial example, but it serves to highlight the problem of just which differences in function should be taken to constitute a reference class. Human beings and other creatures function similarly and differently from each other in a myriad of more and less subtle ways. This produces a great number of potential reference classes, which could be composed of anything from very large to very small numbers of people (Cooper, 2002). Diabetics and people with Down syndrome also have functional characteristics that covary: insulin resistance, hyperglycemia, and poor circulation for diabetics, and trisomy 21, almond-shaped eyes, and flat noses for people with Down syndrome. This uniformity is what makes the description of diseases and syndromes possible. The pathology as described in pathological texts is as uniform as the anatomy described in anatomical texts (Kingma, 2007).

Lastly, if design is taken to mean “written in the genes,” then “Masculinity, Down’s syndrome and Huntington’s disease are all written in the genes” (Kingma, 2007, 130). Kingma argues that these appeals to what is natural, uniform, or designed do not provide an objective and value-free way to distinguish between those functional differences that are constitutive of reference classes in the BST and those that are not.

As an interpretation of “design,” Kingma (2007) entertains the possibility that the notion of “Nature’s intent” might be used to objectively define reference classes. “This should capture the idea that Nature intended there to be men and women, but it did not intend blind people” (Kingma, 2007, 130). Accepting that there is no God to supply nature with purpose, “Nature’s intent” would presumably have to be interpreted in some evolutionary sense. Kingma argues that this runs counter to Boorse’s theory, because Boorse explicitly rejects the relevance of evolution to concepts of health and disease (Boorse, 1976; Kingma, 2007).

Perhaps Boorse’s theory could be amended to define reference classes using an etiological notion of function,¹ before switching to his preferred goal-directed account of function to define disease. On this view, reference classes would be composed of people whose parts evolved to do the same things, and functions would be the contributions of those parts to the apical goals of survival and reproduction typical for those reference classes. Even though reference classes would still be defined in terms of function, and function in terms of reference classes, each of the accounts of function used would be different, and the argument would not be circular. However, this would make disease status a function of how things were in the evolutionary past, and not solely a function of how things are in the present, which is against the spirit of the BST.

Alternatively, perhaps the recognition that people cannot reproduce (and thus achieve one of their apical goals) on their own could assist in the definition of reference classes. Reference classes need to recognize sex differences because these groups are biologically necessary for reproduction, and because their distinctive functional characteristics serve the purpose of reproduction. Species differences might need to be recognized because species are groups of individuals whose offspring can reproduce. Diabetic physiology (or other pathophysiology), however, would not be a reference class, because diabetics are not required for survival or reproduction of the organism. Perhaps, then, goal-directed covariance of functional characteristics might help capture reference classes.

Sadly, the reference-class problem cannot be resolved so simply. Consider a woman born without a uterus. When physiologists study her physiology, they would find that she is not organized toward the apical goal of reproduction. If one of the apical goals of her species is to reproduce, then she is not functioning properly, but remember that the apical goals of her species are supposed to be discovered empirically. Discovering that this woman’s physiology is not organized for reproduction might just as well show that some members of the human species are not organized for reproduction, rather than showing that this woman is dysfunctional. The same can be said for differences in functioning that affect survival, such as diabetes. Their discovery might just as well show that some members of the human species are not organized toward survival in the same way as others are, but not that they are dysfunctional. The reference-class problem is not simple to resolve. “In summary, then, neither natural nor uniform nor design seem to provide Boorse with an objective justification for his selection of reference classes” (Kingma, 2007, 131).

Kingma therefore argues that Boorse has failed to provide a purely empirical, entirely objective way to identify the differences in function that should constitute reference classes. Consequently, she argues that value judgments must be involved in the decision to employ some reference classes rather than others.

Boorse gives no empirical justification for using the reference classes he proposes rather than others; although facts determine both that I am a woman and that I am short-sighted, there are no empirical facts that determine that ‘women’ is an appropriate reference class, and ‘short-sighted people’ is not. Because the choice of reference classes determines the distinction between health and disease on the BST, and Boorse gives no empirical fact that justifies the choice of these reference classes over others, there is no empirical fact that determines the distinction between health and disease on his account. The BST therefore fails to be an empirical or value-free account of health. (Kingma, 2007, 130–131)

Kingma argues that the failure to provide reasons for the BST’s selection of reference classes leads to the production of circular arguments when it is used. Because there are no reasons for using a certain set of reference classes, their use amounts to an assertion that they are the correct ones to use. As Kingma points out, “the choice of reference classes determines the distinction between health and disease on the BST” (2007, 131). Therefore, the assertion that the BST’s reference classes are correct amounts to the assertion that differences in functioning typical for age, sex, and species are healthy; and to the assertion that all other differences in functioning are unhealthy. The distinction between health and disease is asserted by the BST from the outset; it assumes what it claims to demonstrate. “The BST does not give a real answer, let alone a nonevaluative answer, to such a question. Instead, it presupposes the answer it gives” (Kingma, 2007, 132).

Boorse (2014) has replied to Kingma’s (2007) arguments, but his reply is unsuccessful (Werkhoven, 2020). Boorse maintains that the BST is not value-laden, because all the concepts used in it to analyze health and disease—statistical normality, survival, reproduction, organism, part, process, species, sex, age, and causation—are themselves not defined using evaluative language, such as the words “good” or “bad” (Boorse, 2014). This argument is inadequate. If all that was required for a theory of health and disease to be objective was freedom from explicit value judgments, then all the alternative theories of health considered by Kingma (2007) are just as value-free as the BST. Cataracts, myopia, and trisomy 21 can be defined without evaluative language, just as age, sex, and species can be. Kingma’s XST, which is exactly like the BST, except that it recognizes homosexuals as a reference class, can be articulated using the concepts of statistical normality, survival, reproduction, organism, part, process, species, sex, age, causation, and sexual intercourse. The decision to use the BST or not would still depend on a prior evaluation of what counted as a disease, allowing what counts as a disease to vary with human value judgments. If he wants to maintain that “the classification of human states as healthy or diseased is an objective matter, to be read off the biological facts of nature without need for value judgements” (Boorse, 1997, 4), then Boorse cannot allow concepts of function or disease to vary with value judgments, whether or not these value judgments are made explicitly. As Shane Glackin argues²:

It is a truism, undenied by any normativist I am aware of, that we can state the extension of the concept ‘disease’ in value-free terms of greater or lesser abbreviation; what is at issue is whether we can say why these—and not others—are the diseases without appealing to social facts and human evaluations. If we can, then constructivism is superfluous. If we cannot, naturalism is false. (2014, 416)

It is clear from how Boorse has replied to other areas of criticism that he understands this. Even though the concepts of survival and reproduction can be defined without evaluative language, Boorse feels the need to defend the BST against the criticism that the choice of these things as the apical goal of an organism is just that, an evaluative choice. Boorse does not just dismiss these criticisms by saying that “it does not matter at all how concept H [health] was ‘chosen,’ only what it is” (1997, 23–26), as he does for arguments about the value-ladenness of reference classes. He argues that there is no choice to be made here, because the study of human bodies as organized systems reveals that they act to promote their survival and reproduction (Boorse, 1997). The centerpiece of Boorse’s theory is that apical goals are discovered empirically, not chosen for evaluative reasons. This wonderful argument would be redundant if all that Boorse wants to defend is the freedom of his theory from evaluative language. That Boorse makes this argument shows he is aiming at a more comprehensive form of value freedom and objectivity, which he has failed to articulate in his theory of reference classes.

Sander Werkhoven has tried to defend the objectivity of reference classes from Kingma’s arguments. He argues that Kingma has confused the justification of the BST with the meaning of the terms used by it (2020, 150). Werkhoven argues that it is legitimate to know which people are healthy and which are diseased during the process of demonstrating that a theory of health and disease provides a good description of medical practice. “To justify the choice of a philosophical theory, one may refer to all sorts of antecedently held beliefs about the phenomenon in question” (Werkhoven, 2020, 150). Indeed, in order to produce such a description, the ability to distinguish health and disease seems necessary. Werkhoven concedes that if the meaning of the terms used in the theory could not be understood without prior knowledge of health and disease, then the BST would be illegitimate. He maintains, however, that “if one inquires further into what is meant by ‘statistical normality,’ ‘functioning of parts,’ or ‘a reference class,’ perfectly intelligible answers can be given that do not presuppose knowledge of the health/pathology distinction” (Werkhoven, 2020, 150).

This defense, however, fails. As discussed, Kingma is not arguing that the justification of the BST is circular. Rather, she is arguing that the use of the BST to justify the view that a given individual has a disease (or is healthy) results in a circular argument. As Boorse has failed to justify the BST’s reference classes, Kingma argues he has just asserted that these are the correct ones to use when determining disease status. Kingma notes that the choice of reference classes determines the distinction between health and disease. The assertion of what can and cannot count as a reference class at the beginning of the BST is also the assertion of what can and cannot count as a disease at its end. Even if the terms used by the BST can be defined without reference to the distinction between health and disease, the assertion of what the correct reference classes are still results in circular arguments when the BST is used to distinguish health from disease.

Furthermore, Werkhoven’s defense assumes that the meaning of “reference class” is exhausted by the terms “age,” “sex,” and “species.” This ignores the role that the phrase “a natural class of organisms of uniform functional design” plays in providing reference classes with meaning. The possibility that the BST’s interpretation of what this means incorporates judgments of what it is to be healthy should be taken seriously. This phrase defines different reference classes in terms of differences in biological functioning. The question of which reference classes to use becomes a question of which differences in biological functioning should be constitutive of reference classes. Age is taken as constitutive of reference classes because there are differences in functioning associated with aging that are taken as constitutive of reference classes. Boorse notes that how humans function changes as they age, but why should these differences in function, and not others, constitute reference classes? For example, premenopausal women function differently to postmenopausal women, but why does this indicate that age-related functional differences are constitutive of reference classes? As discussed, these are no more natural, uniform, or designed than differences in function not taken as constitutive of reference classes. Even ignoring species differences, the menopause is not statistically normal, as only around half of humans go through it. To argue that the menopause is relevant to the constitution of reference classes because it is statistically normal for women is to put the cart before the horse. Relevant differences in function, like the menopause, are supposed to be evidence that sex differences are constitutive of reference classes. That sex differences are constitutive of reference classes is not supposed to be evidence the differences in function, like the menopause, are relevant. In any case, with the queen bee in mind, would it really matter if only a tiny proportion of humans functioned as women do? Would the infrequency of feminine functioning mean that such differences were diseases? Given these difficulties, might it be that the menopause is considered constitutive of a reference class because it is taken to be a normal and healthy part of aging? If so, the circularity of the BST regarding the meaning of the terms it employs would become manifest. Some functional differences are taken to be healthy and used to define reference classes; others are taken to be diseases and are not used to define reference classes. Given this, to claim that those functional differences that are not used to define reference classes are diseases is to argue in a circle.

Ironically, Werkhoven makes this argument while attempting to defend the BST from it. “What I am suggesting, then, is that we have an intuitive grip on the sort of conditions that could be healthy or pathological, and these conditions cannot constitute a reference class” (Werkhoven, 2020, 155). This is exactly Kingma’s concern. If intuitions direct us not to question the view that a difference in functioning is healthy, then it is allowed to serve as a reference class. If our intuitions direct us to suspect that a thing may be a disease, then it is not allowed to serve as a reference class. If intuitions about what is and is not healthy are allowed to inform what counts as a reference class, then the meaning of a reference class is linked to these intuitions, and so are the BST’s judgments about who is diseased. If Werkhoven’s suggestion is correct, then the BST does not confirm or refute our intuitions, so much as just restate what our intuitions are. Appealing to intuition does not provide a satisfactory basis for claims of objective knowledge.

Werkhoven also rejects Kingma’s argument that the BST is value-laden. He correctly states that Kingma’s (2007) conclusion is that the BST is value-laden. However, his presentation of her argument is incorrect. Werkhoven provides five premises that Kingma supposedly uses to support her conclusion, with the “crucial premise on which Kingma’s argument hinges” being “pathological conditions and healthy conditions are differentiated . . . on the basis of cultural norms about how people ought to be” (Werkhoven, 2020, 151–153). Boorse (2014) also reads Kingma as assuming from the outset that health and disease are differentiated on the basis of cultural norms. But this is not Kingma’s argument. Kingma’s argument is that if the BST does not justify the distinction it draws between health and disease entirely empirically, then it is value-laden. She uses her analysis of reference classes to argue that the BST does not do this, and therefore concludes that the BST is value-laden. Only following this does she suggest that these values may reflect cultural norms about how people ought to be. “The fixing of reference classes, however, is an evaluative choice which may reflect some deep underlying normative commitments” (Kingma, 2007, 132). The suspicion that such cultural norms determine the distinction between health and disease is not assumed by Kingma (2007), but rather is an attempt to fill the epistemological vacuum left by the BST’s deficient theory of reference classes.

Following Boorse, Werkhoven also points to diseases that are valued to demonstrate that the distinction between health and disease is not evaluative in the way Kingma suggests. If the distinction between health and disease is made on the basis of evaluative judgments, then healthy conditions will be positively valued and pathological conditions will be negatively valued. Given this, there should be no positively valued pathologies, and no negatively valued states of health. As this is not so, Werkhoven argues that the distinction between health and disease cannot be made on the basis of value judgments. Again, however, Kingma’s argument does not rely on this assumption, and neither is it her conclusion. Showing that some pathological conditions are valued in some way just rules out the possibility that all pathological conditions are defined as disvalued conditions. This does not rule out the possibility that evaluative judgments are involved in making the distinction between health and disease in some more subtle way. This should be taken as an invitation to investigate carefully how values inform the choice of reference classes, which I now do by exploring the definition of low bone mineral density in children.

III. AGE-ADJUSTED REFERENCE CLASSES: THE Z-SCORE

Osteoporosis is a disease of increased bone fragility associated with low bone mineral density. In adults, osteoporosis is diagnosed by measuring bone mineral density, using dual energy x-ray absorptiometry (DXA or DEXA), which has been common since the 1980s (Wylie, 2010). If the function of bone is to be strong and light enough to permit movement, bone mineral density is not itself a direct measure of bone function. Bone is a complex material (Felsenberg and Boonen, 2005). While many tissues are made mostly of cells, with small amounts of extracellular matrix, bone tissue is mostly extracellular matrix with a smaller number of cells. This extracellular matrix is mineralized, making the bone hard. Long bones are composed of solid cortical bone that acts as a hard outer shell, which encases regions of trabecular bone that have a honeycomb or scaffolding-like structure. The strength of the bone depends not just on the quantity of mineralized tissue, but also on the quality of the mineralized tissue and its configuration within the bone (Baroncelli et al., 2005; Felsenberg and Boonen, 2005). “Bone densitometry provides surrogate measures of bone strength” (Rauch et al., 2008, 25). Even so, bone mineral density is used to assess bone strength. “Indeed, BMD [bone mineral density] accounts for 75–85% of the variance in the ultimate strength of bone tissue” (Baroncelli et al., 2005, 297).³

The density of something is usually thought of as the amount of material in a given volume. This is called volumetric density. DXA does not measure volumetric density. DXA shoots x-rays across the shaft of a bone, measuring the amount of mineral present from the degree to which the x-rays are absorbed by the mineralized tissue (see fig. 1). The more mineralized tissue, the greater the absorption. Although the area through which the x-ray beam passes can be measured, DXA has no means to assess the thickness of the bone through which it passes. DXA measures the amount of mineral under a given area of bone, and not the amount of mineral in a given volume of bone. This is called areal bone mineral density.

Fig. 1.

Areal bone mineral density. An x-ray beam travels through the shaft of a bone, making contact with an area on the surface of the bone as it does so (the 'Area of Contact'). DXA measures the amount of bone mineral in the path of the x-ray beam under that area. The thicker the bone (the greater the depth dimension), the more mineral there is in the x-ray beam’s path, even if the area of contact remains the same.

A larger person may have bones that are larger in all three dimensions, length, width, and depth. Under the same area of bone, under the same length times width, a larger person may well have more bone because of the greater thickness of bone, the greater depth dimension (see fig. 1). So, the areal bone density of a larger person could well be greater because of the increased thickness of bone, even if volumetric density is the same. All things being equal, thicker bones are stronger bones (Schoenau et al., 2004; Srinivasan et al., 2012; Binkley, Adler, and Bilezikian, 2014). In adults, areal bone mineral density is correlated with fracture risk, and is used to assess osteoporosis. Unless otherwise stated, when referring to bone mineral density, I am referring to areal bone mineral density.

To decide whether or not a person has low bone mineral density, their bone mineral density must be compared to some standard value. The average bone mineral density of a reference class is often used as this standard value. But which reference class should be used? Two possibilities are an age-adjusted reference class, which would compare individuals to people of the same age, or a young reference class, where people are compared to young adults even if they are elderly. As it happens, physicians use both of these reference classes in different circumstances. Sometimes, they use the age-adjusted reference class to produce what is called a Z-score; and sometimes they use the young adult reference class to produce what is called a T-score.

Many physicians argue that using age-adjusted reference classes to judge the bone mineral density of older patients is inappropriate, because this does not allow the prediction of fragility fractures in older patients (Odvina et al., 1988, 227; Kanis et al., 1994, 1137–1138). For postmenopausal women and men over 50 years of age, the World Health Organization (2007) recommends using the T-score (with the young reference class). For younger adults and children, they say the Z-score (with the age-adjusted reference class) should be used.

T-scores should be reserved for diagnostic use in postmenopausal women and men aged 50 years or more. With other technologies, and other populations, measurement values should be expressed as Z-scores, units of measurement, or preferably in units of fracture risk. (WHO, 2007, 8)

The situation regarding the diagnosis of low bone mineral density and osteoporosis in children is different from that in adults. Around the turn of the twenty-first century, physicians did understand osteoporosis in children as being low bone mineral density (Saggese, Baroncelli, and Bertelloni, 2001; van der Sluis and de Muinck Keizer-Schrama, 2001). However, while physicians do use low bone mineral density to diagnose osteoporosis in adults, the ability of low bone mineral density to evaluate fracture risk in children is less powerful and less well understood than in adults (Laine and Laine, 2013; Ward et al., 2020). Consequently, many physicians argue that osteoporosis should not be diagnosed in children unless the fragility of the skeleton is proved by the presence of fragility fractures (Gafni and Baron, 2004; Rauch et al., 2008; Wasserman, O’Donnell, and Gordon, 2017). Even so, other physicians have concerns about this approach, because they are worried it will fail to identify patients with fragile skeletons who have yet to fracture. Such physicians argue that low bone mineral density should be used along with several other parameters to assess skeletal fragility (Ward et al., 2020).

Physicians do not only measure bone mineral density to assess skeletal fragility during childhood. They also measure bone mineral density in children to predict skeletal fragility in adulthood. Bone mineral density in human beings typically rises during childhood, to a peak in young adulthood, after which it starts to fall again. Physicians are concerned that people who do not acquire enough bone mineral during childhood may not attain a high enough peak bone mineral density in early adulthood to prevent the development of osteoporosis in later life. “Although the medical community recognizes the considerable impact of this disease on adulthood, many primary care providers do not realize that osteoporosis has its origins in childhood and disorders of bone accrual are often ignored” (Gordon et al., 2017). “Senile osteoporosis is a paediatric disease” (van der Sluis and de Muinck Keizer-Schrama, 2001; quoting from Dent, 1973). The condition I am concerned with in this paper is low bone mineral density in childhood.

I show how physicians do use age, sex, and race to define reference classes in the diagnosis of low bone mineral density in children, as the BST requires (see Low bone density in children: age-, sex-, and race-adjusted reference classes). However, I also show that they use body size, muscle mass, pubertal age, bone age, and height age to do the same, in conflict with the BST (see Pubertal age, size, bone age, and height age). Even if the use of these additional factors goes against what the BST says about how to define reference classes, these physicians do attempt to justify some of their choices of reference class by appealing to how the human body functions, which is at least in keeping with the BST (see Functional accounts of pubertal age and body size). However, I show that physicians also calibrate their reference classes according to their prior knowledge of health and disease, as critics of the BST say they might (see Health-adjusted reference classes). I close by showing that physicians also choose reference classes according to the ability to assess the risk of fracture (see Pragmatic solutions to continuing challenges for assessing bone mineral density). Physicians even suggest that different reference classes need to be used to achieve different clinical goals, subordinating naturalistic arguments about reference classes to pragmatic considerations.

Low Bone Density in Children: Age-, Sex-, and Race-Adjusted Reference Classes

The importance of using an age-adjusted reference class is most apparent from medical literature on the misdiagnosis of childhood low bone mineral density. Some children are diagnosed with low bone mineral density based on their T-score: a low bone mineral density relative to the young adult population. Specialists argue that this is inappropriate, and a common error. “The most frequent interpretation error was the use of the T-score rather than the Z-core” (Gafni and Baron, 2004, 255). They make this argument because a child’s skeleton is still growing and mineralizing, and it should not be compared to that of an adult:

In children, however, interpretation of DEXA is complicated by issues related to ongoing bone growth and bone mineral accrual. The measurement of BMD that is derived most commonly from DEXA depends on skeletal size. As a result, the T score, which compares a person’s BMD with young adult normative data, should not be used for children who have not completed either their linear growth or their bone mineral acquisition. The Z score (SD score compared with persons of the same age) is more useful. (Gafni and Baron, 2004, 253)

These physicians also argue that reference classes should take account of the child’s sex. Again, this is sometimes forgotten when diagnosing osteoporosis in children, as physicians compare bone mineral density measurements of children with reference data that does not distinguish between males and females.

Another common interpretation error involved the use of a pediatric reference database that does not differentiate between boys and girls. Because the BMD of normal boys and girls differs, particularly in early adolescence, the use of these databases can lead to misinterpretation. For example, peripubertal boys may factitiously appear to have low BMD if compared with girls of the same age. (Gafni and Baron, 2004, 256)

These arguments are in close agreement with the BST. These physicians advise assessing bone mineral density relative to age and sex. They also mention race as relevant to reference class selection (Gafni and Baron, 2004), again in agreement with the BST. Even if more work needs to be done to provide a theoretical basis for the BST, this does provide some empirical support for it.

Pubertal Age, Size, Bone Age, and Height Age

Intriguingly, these physicians take other factors, in addition to age, sex, race, and species, as relevant to the definition of reference classes. For example, they also discuss pubertal status and body size as important. “[T]he DEXA software for pediatric patients should use normative data specific for age, sex, ethnicity, and, ideally, body size and pubertal status” (Gafni and Baron, 2004, 256). Body size can be assessed according to height, weight, and lean muscle mass (Jones, Ma, and Cameron, 2006). Pubertal stage can be assessed using the patient’s Tanner stage, which allocates boys and girls to five categories of pubertal development according to sexual characteristics such as mammary development, testicular development, and growth of pubic hair (Arabi et al., 2004). Each Tanner stage could be seen as its own reference class, with a patient having, for example, a reduced/normal/increased bone mineral density for a male in Tanner stage 1.

Children grow at different rates, and go through puberty at different times, so body size and pubertal status are not the same as chronological age. The decision to take these factors into account, or not to, might influence whether a patient’s bone mineral density is seen as reduced or not. Smaller children tend to have lower bone mineral density as assessed by DEXA (see below). Healthy children who are just small for their age would appear to have low bone mineral density if their body size is not taken into account. Similarly, children who are large for their age may appear to have normal bone mineral density for their age, but have low bone mineral density for their size. Thus, “in children who are unusually small or large for their age, age-specific normative data may not be appropriate” (Gafni and Baron, 2004, 255). At puberty, the increase in sex hormone production leads to increased skeleton growth. “Thus, delayed puberty could be considered a cause of mild, reversible decreased volumetric BMD [bone mineral density]. However, if one compares the child with normal children of the same pubertal stage, one would consider the BMD normal” (Gafni and Baron, 2004, 255–256). Decisions about which of these factors should be used to define reference classes can affect the diagnosis of low bone mineral density.

Pubertal status can be understood as a different way of measuring age. Children in the same Tanner stage could be understood as being the same pubertal age, even if they have been alive for different amounts of time. Instead of focusing on chronological age, physicians may choose to focus on pubertal age. Differences in height have also been understood in this way, and presented as height age: the age that corresponds to the child’s height when plotted at the 50th percentile on a growth chart (Herzog et al., 1998). Say that the median height of 8-year-old boys is 125 cm. If a 10-year-old boy is 125 cm tall, then his height age is eight. Bone age is yet another way to understand age. Bone age is assessed by comparing the radiographic pattern of ossification of a child’s wrist with those in an atlas showing the typical development of children’s wrists at different ages. If a 10-year-old child’s wrist looks like the typical 8-year-old child’s wrist, then the child’s bone age is eight.

Bone age is an indicator of the skeletal and biological maturity of an individual. This is different from chronological age, which is calculated using the date of birth of an individual. Bone age is often requested by pediatricians and endocrinologists for comparison with chronological age for diagnosing diseases which result in tall or short stature in children. (Mughal, Hassan, and Ahmed, 2014, 211)

These different ways of assessing age are used to evaluate whether a patient’s bone mineral density is appropriate for their biological age, rather than for their chronological age. Even so, body size, pubertal status, height age, and bone age are all different from each other, and different from chronological age. Choosing to use any of them, and not others, would produce different concepts of disease. This goes against the BST.

Functional Accounts of Pubertal Age and Body Size

However, attention to body size, pubertal status, and other indices of biological age may be interpreted to count in favor of the BST as well. The reason that Boorse argues that age is relevant to reference classes is because certain differences in functioning form part of the biological life stages of humans as they age. The process of becoming sexually mature seems a strong candidate for a transition between such life stages, and these physicians are paying attention to such life stages in their work. Pubertal status, assessed using Tanner stage or bone age, may be a better way of measuring biological age than chronological age.

Using body size to define reference classes may go against what the BST says about reference classes, but it may also be commensurate with its spirit. Physicians recognize this problem about how to define disease due to low bone density, and propose a functional solution to it. “How, then, can densitometric data in children and adolescents be evaluated in a rational way? We propose a functional approach to this fundamental problem” (Schoenau et al., 2004, s90). A lovely interspecies comparison illustrates this functional proposal:

Mice have a lower bone mass than elephants. Therefore, mice will be diagnosed as osteoporotic when age-matched elephant standards are used as a reference. However, there is no evidence that mice have more fractures than elephants. As Galileo Galilei commented in the seventeenth century, small bones perform the same function in small animals as large bones in large animals. The same should apply to small and tall children, adolescents, and adults. (Schönau, 2004, 828)

The solution these researchers suggest is to conceive bone and muscle together as a functional unit. They propose a two-stage diagnostic process. First, they determine whether a patient has adequate muscle mass for their height, and then they determine whether the patient has adequate bone mineral content for their muscle mass. Patients are diagnosed with low bone mineral content if they do not have adequate bone mineral content for their muscle mass, or if they do, but have low muscle mass for their height (Schoenau et al., 2004, s90).⁴ “Based on such simple ideas, it can be reasonably suggested that analyses of bone mass (and bone structure) should focus on the question of whether they are adequate for bone function” (Schoenau et al., 2004, s91).

Others make similar comments, arguing that “The human body tries to adapt bone mass and bone geometry to body height and weight and not to age” (Gökşen et al., 2005, 466). Physicians also point out that muscle mass and bone mass are tightly correlated, supporting the view that bone and muscle act as a functional unit. “Several studies have shown that there is a high correlation between muscle mass and bone mass in children, consistent with the functional bone-muscle unit theory” (Crabtree et al., 2013, 232). Here, we find physicians thinking about the appropriate level of bone mineral content/density in terms of what nature might have “intended” bones to do: support the muscles. It may be necessary to account for body size when assessing bone mineral density because of the way the human body functions. Making such functional arguments about how to define reference classes is in keeping with the spirit of the BST, even if references classes are not used in the way the BST says they should be.

Debates about how the function of bone should be understood raise questions about just what the function of bone is and how it should be measured. If a function of bone is to be strong enough to support movement (without becoming so heavy as to prevent movement), then some of the adjustments for body size might reflect attempts to compensate for our inability to measure bone strength properly, rather than the creation of new reference classes. Many physicians who argue for body-size-specific reference classes see volumetric bone mineral density as the “true” bone mineral density that should be used to diagnose disease (Bertelloni et al., 1998; see also Klaus et al., 1998; Gökşen et al., 2005). If volumetric density is the true bone mineral density, then differences in areal density might be “artefacts” (Schoenau et al., 2004, s87), which can be corrected by taking body size into account. If we take volumetric bone mineral density to represent the true function of bone, then the decision to use body size to define reference classes can be understood as an effort to correct the deficiencies of areal bone mineral density as a surrogate for the function of bone. Physicians might be trying to transform areal density into volumetric density by dividing areal density by a dimension that tracks the thickness of bone, such as body size. Body size, assessed using height or weight, need not be understood as defining new reference classes, but rather as compensating for the inability to assess biological function properly.⁵

It is not immediately clear, however, why volumetric bone mineral density should be understood as a better surrogate of bone function than areal density. Areal bone mineral density is used to diagnose osteoporosis in adults, after all. With equal volumetric bone density, people with greater areal density will have more bone, and, other things being equal, stronger bones (Schoenau et al., 2004; Srinivasan et al., 2012; Binkley, Adler, and Bilezikian, 2014). “Thus, this variable (areal BMD) integrates not only the amount of mineral but also indirectly the dimension of bone. The high level of prediction of bone strength by areal BMD could be at least partially explained by the fact that bone size is indirectly integrated in this measurement” (Ammann and Rizzoli, 2003, s14). Researchers have found that many different ways of measuring bone density assess breaking strength equally well. “In summary, BMC, areal BMD, volumetric BMD, and volumetric BMAD were valid and comparable surrogates of the breaking strength of bone in vitro” (Tabensky et al., 1996, 1987). If one of the functions of bone is to be strong, then it is not clear that areal density does not measure the functional status of bone.⁶

Perhaps volumetric and areal density are both lower-level functions that serve the higher-level function of bone strength. Perhaps low volumetric density can be compensated for by high areal density, making the amount of mineral in a given length of bone (or bone mineral content) the correct measure of the function of bone. Perhaps these are all poor surrogates for bone function, which can only be assessed by more sophisticated imaging techniques (such as quantitative computed tomography) that can measure the mass, composition, areal density, and volumetric density of bone, as well as the quantity and quality of both cortical (solid-outer-shell) and trabecular (honeycomb-inner-structure) bone. There are a dizzying number of ways that the function of bone could be cashed out.⁷

What ultimately gets used to measure the function of bone influences the interpretation of what reference classes are being used to define disease. If bone density is understood as the function of bone, then assessing bone density according to (e.g.) muscle mass makes muscle mass into part of the definition of a reference class. Alternatively, arguing that the function of bone is to support the muscles, and using bone density for muscle mass to measure the function of the musculoskeletal system, makes muscle mass part of the definition of a function, and not part of the definition of the reference class. This illustrates the very close relationship between functions and reference classes that exists in the BST because of the way functions are defined in terms of reference classes, and reference classes are defined in terms of function, as critics of the BST have argued.

Health-Adjusted Reference Classes

Even if examples can be found of physicians arguing about the appropriate reference classes to use in terms of biological function, they also argue about reference classes in ways that are radically at odds with the spirit of the BST. Some physicians studying populations of children with small stature refer to these children as “normal,” or as “healthy” (Bertelloni et al., 1998; Schoenau et al., 2004). Children of small stature for their age often have lower areal bone mineral density, even though they have normal volumetric density, and normal areal bone mineral density for their size. Consequently, assessing these children’s areal bone mineral density for their age identifies a lot of children who are thought to be healthy as having low bone mineral density. “Using age related reference data would produce a lot of ‘healthy’ children with osteopenia” (Schoenau et al., 2004, 151). The use of inverted commas around “healthy” by these physicians is a manifestation of the reference-class problem. If judged against children of the same sex and age, then smaller children with lower areal bone mineral density would have a disease. If judged against children of the same size, however, they would not have a disease. As the small stature of these patients has been designated healthy, the finding that these children have decreased areal bone mineral density is not taken to be a sign of disease by these physicians. Just as Kingma (2007) hypothesized, decisions about which differences count as diseases and which do not are being reflected in choice of reference classes.

This point is made forcefully by seeing that physicians calibrate their reference classes according to their knowledge of who is healthy and who is diseased. For example, some researchers have sought to investigate the reduction of bone mineral density seen in patients with Crohn’s disease. Crohn’s disease is known to produce calcium malabsorption and vitamin D deficiency, and produce inflammatory responses, which act to inhibit bone formation (Herzog et al., 1998). The corticosteroids used to treat Crohn’s disease also diminish bone mineral density. But to what extent? When chronological age was used to define reference classes, evaluating the bone mineral density for boys and girls of the same chronological age, these researchers found that 44% of the Crohn’s disease patients they studied had low bone mineral density. However, these researchers argued that this was not the true prevalence of low bone mineral density among these patients.

These researchers point out that bone mineral density varies in healthy children, and that this variation is positively correlated with differences in body size and pubertal stage. “Good correlation has been observed between BMD and age, height, weight, and pubertal stage in normal children and adolescents” (Herzog et al., 1998, 261). So, children with lower bone mineral density tend to be shorter, lighter and at an earlier stage of pubertal development than children with higher bone mineral density. This means that if researchers take account of these differences in height, weight, and pubertal stage, these differences in bone mineral density in healthy children disappear. This finding is understood to show that children with low bone mineral density can be healthy so long as their bone mineral density is normal for their body size and pubertal stage. Indeed, these researchers refer to correcting Z-scores produced using chronological age by using bone age or height age instead. “The aim was to compare z-scores for BMD in relation to CA [chronological age] and z-scores corrected for BA [bone age] or height age in pediatric patients” (Herzog et al., 1998, 261). These researchers argued that the correlation between bone mineral density and bone age or height age in healthy children meant that these should be used instead of chronological age to define reference classes. “This correction is moreover justified by two studies in normal children, which examined the correlation between BMD and growth parameters. BMD was found to be highly correlated with BA” (Herzog et al., 1998, 265).

These researchers note that patients with Crohn’s disease often have stunted growth and pubertal delay. Consequently, they suggested that using chronological age to define reference classes in Crohn’s disease patients would “result in falsely low BMD values” (Herzog et al., 1998, 261). Following “correction,” the prevalence of low bone mineral density fell from 44% to between 26% and 30%, depending on whether the Z-score was corrected for bone age or height (Herzog et al., 1998, 266). These lower values were taken to more closely reflect the true prevalence of low bone mineral density in these patients.

As another example, consider researchers who sought to explore the effect of renal transplantation in children with chronic renal failure on their bone mineral density (Klaus et al., 1998). Patients with chronic renal failure often have stunted growth and decreased bone mineral density as measured. These researchers knew that, in healthy children, bone mineral density is closely correlated with body size. This made them wonder about how best to evaluate bone mineral density in children.

An association between height and bone mass is well established in healthy children and adolescents, as illustrated by the parallel increase of BMD and height velocity in very young children and at the time of puberty. The population of transplanted children is significantly growth retarded. We therefore addressed the question of whether BMD in pediatric patients is also reduced when corrected for actual body height and weight. (Klaus et al., 1998, 343)

Because of the association between bone mineral density and height and weight in healthy children, they argue that assessing a child’s bone mineral density for its chronological age is inadequate. “If one measures areal BMD in a patient population with a diminished height and weight for age, comparison of areal BMD with age-related controls is not a gold standard” (Klaus et al., 1998, 345–346). Consequently, they investigated whether the reduction in bone mineral density seen in their patients persisted, following correction for body size (Klaus et al., 1998). Following this correction for body size, they found that the reduction in bone mineral density disappeared in their patients. “The present study demonstrates for the first time that areal BMD measurements in growing children after Tx are reduced only when related to chronological age and not when corrected for statural height or weight” (Klaus et al., 1998, 345).

These researchers see differences in bone mineral density among healthy patients, which can be accounted for by assessing bone mineral density relative to body size and pubertal status in addition to age, sex, and species. With these differences accounted for, the differences between the “healthy” children disappear, indicating to these physicians that they had calibrated their reference classes correctly—that they had taken account of all the healthy differences in functioning. Having done this, all other differences in functioning could be assigned to the effect of the various pathological conditions explored. The differences due to the pathological conditions, however, were not taken into account, precisely because these were known to be pathological conditions. These physicians calibrated their reference classes using their knowledge of who is healthy and who is diseased. This is exactly what concerns critics of the BST. These are not simply age-adjusted reference classes, they are health-adjusted reference classes.

Pragmatic Solutions to Continuing Challenges for Assessing Bone Mineral Density

It may be that none of the different reference classes used by physicians are universally applicable. Physicians point out circumstances under which each of the ways of correcting for pubertal status and body size might be inadequate. So, even though bone age is related to pubertal status in healthy children, there are circumstances under which correcting Z-scores for bone age will be misleading (Crabtree et al., 2014). In patients with genetic short stature, for example, bone age is much older than height age. Because these smaller children have thinner bones and low areal bone mineral density, if bone age is used to define their reference class they will be compared to children with a similar bone age who are taller and have thicker bones with higher areal bone mineral density. Such children appear to have low areal bone mineral density for their bone age, even though this could be thought of as normal for their size. “Therefore, caution should be used when substituting bone age for chronologic age in calculating Z-score, as bone age may not correct for bone size in this setting” (Crabtree et al., 2014, 231).

Using height to define reference classes, however, produces similar problems. If children are compared to other children of the same height, such as chronically ill patients with stunted growth (such as those with cystic fibrosis) in comparison to younger, normally growing children, perhaps then the bone mineral density of the chronically ill children are made to appear more normal than it should (Conway et al., 2008). “Caution should be used when correcting for body size using height and weight as normal healthy children will tend to be younger than chronically ill children when matching for height and weight” (Conway et al., 2008, 473). Similarly, comparing children of the same height may lead to short, postpubertal children being compared to tall, prepubertal children, making the prepubertal children’s bone mineral density appear artificially low, and the postpubertal children’s bone mineral density appear artificially high. “This practice is especially worrisome if a short pubertal child is compared with a prepubertal child, highlighting the critical role of pubertal development on bone accretion during adolescence” (Crabtree et al., 2014, 232). The problem here is that physicians have not found a way to correct bone mineral density that does not sometimes makes a person whom they consider healthy appear as though they are diseased, or that makes a person they consider diseased appear healthy. These considerations depend on prior knowledge of health and disease, which physicians use to identify problems with different reference classes. This forces physicians to consider using different reference classes in different circumstances.⁸

Adjusting for muscle mass also generates problems. As discussed above, physicians do make functional arguments in support of assessing bone mineral density relative to muscle mass or lean body weight, but they also recognize scenarios where this is inappropriate. For example, if children have low muscle mass, they may have adequate bone mineral density to support this muscle mass, but still have weak bones. “If one adjusts for muscle, the bones will look ‘normal’ but in reality are not. One should report the unadjusted bone result to show that the bones are weak; then use the adjusted result to suggest that the deficit may be related to the muscle deficits” (Crabtree et al., 2014, 233). This suggests that both taking and not taking muscle mass into account are relevant to the definition of reference classes. Perhaps medics should use several different reference classes, and therefore several different concepts of disease, in quick succession in their practice.

Physicians also call the value of the theory that bone and muscle are a functional unit into question for pragmatic reasons.⁹ Some researchers argue that the ability of bone mineral density relative to muscle mass to predict risk of fracture is unknown, and that this casts doubt on whether this is the correct evaluation to make (Gafni and Baron, 2004; Borges and Brandão, 2006; Crabtree et al., 2014). Others argue that there is evidence that evaluating bone mineral content relative to lean body mass is a poor predictor of fracture risk, which means that this way of evaluating bone mineral content should not be used. “Although BMC divided by lean mass has value as a theoretical concept in categorizing types of low bone mass, it did not perform well in discriminating fracture cases from control and suggested limited utility in children as a whole” (Jones, Ma, and Cameron, 2006, 205). Although the evaluation of bone mineral density/content relative to muscle mass may have a theoretical justification in keeping with the BST, this theoretical justification is overridden by practical concerns about how to predict adverse clinical events. In this case, naturalistic theories are subservient to pragmatic concerns.

This does not only apply to muscle mass. Physicians show a general interest in selecting the factors used to define reference classes according to pragmatic needs. Some physicians have reported that DXA measurements of bone mineral density, and indices calculated using them, are useful for predicting fractures in children (Jones, Ma, and Cameron, 2006; Crabtree et al., 2013; Elhakeem et al., 2019). Such findings have themselves been used to justify the choice of reference class, or reference data set, as the set which best allows the prediction of fractures.

Interest in the clinical utility of DXA-based BMD measurement in children has heightened over recent years, because a growing number of pediatric studies have shown a clear relationship between low BMD and the risk of vertebral and non-vertebral fractures. As a result, the optimal use of DXA-based BMD to identify which children are in need of bone health monitoring is an ongoing point of focus for pediatric bone health care providers, with the ultimate goals being to predict individuals at risk of overt bone fragility and to intervene to prevent fractures.

One of the challenges facing clinicians in the use of DXA for assessing BMD in children is choosing the normative database that will be used to convert raw BMD scores to gender- and age-specific Z-scores. (Ma et al., 2015, 1019)

Even where age- and sex-specific reference classes are used, as in the childhood diagnosis of low bone mineral density, pragmatic considerations such as the prediction of fractures are seen by many physicians as the ultimate standard against which the correct reference class can be chosen.¹⁰

In addition to predicting the risk of fractures in children, physicians argue that bone mineralization in childhood is one of the crucial determinants of peak bone mass in adulthood. Adults with low peak bone mass are themselves at risk of developing osteoporosis and fragility fractures in later life (Arabi et al., 2004; Elhakeem et al., 2019). Physicians are concerned that later puberty can lead to lower peak bone mineral density and higher risks of osteoporosis (Elhakeem et al., 2019). Thus, a child can have normal mineralization for pubertal stage, but be at risk of developing low peak bone mass. It is possible, then, that children may have appropriate bone mineral density for their size or pubertal status, and be of low risk of fracture in childhood, but be on a trajectory to low peak bone mineral density, and thus be at risk of sustaining fragility fractures in later life. Given this, perhaps fracture risk in childhood and in later life should be assessed using bone mineral density relative to different reference classes. For example, if we are trying to determine whether an individual has strong enough bones to support the body during childhood, bone mineral density might be evaluated against muscle mass. If we are trying to determine whether the individual will accrue enough bone mass in childhood to support the body in later life, it might be better to assess bone mineral density against height (or even estimated maximum height). Similarly, assessing bone mineral density for pubertal age or bone age may reflect whether bone mineral density is appropriate for life stage, but assessing against chronological age might be better at keeping track of whether the skeleton is running out of time to accrue sufficient bone tissue to support the skeleton in old age. It is possible that different clinical goals require different reference classes and different disease concepts.¹¹

When considering adjustments of DXA measurements for bone size, height, LBM, skeletal age, or pubertal stage in growing children, it is relevant to consider the goal of the exercise. Aims might include avoiding overdiagnosis (and hence inappropriate treatment) of osteoporosis in children who are small for their age; understanding the etiology of low bone mass (short stature, narrow bones, low bone area, low lean mass); or predicting fracture risk. There is no single adjustment paradigm proven to be optimal to achieve these aims (Crabtree et al., 2014, 233)

Here, an “adjustment paradigm” is the reference class used to evaluate bone mineral density. These researchers suggest that different reference classes may need to be used to achieve different clinical goals.¹² Others have suggested that different reference classes should be used, depending on the type of fracture that one is trying to predict. “In conclusion, vertebral fractures are best predicted by L2–L4 BMAD [bone mineral apparent density] for age and long bone fractures are best predicted by TBLH BMC for LBM [total body less head bone mineral content for lean body mass] adjusted for height” (Crabtree et al., 2013, 2023). Reference classes, and disease concepts, are being selected according to pragmatic interests, not naturalistic arguments.

IV. CLOSING SUMMARY

The reference-class problem presents a significant challenge to Christopher Boorse’s biostatistical theory of health and disease. The BST requires that reference classes be defined objectively as the natural classes of organisms of uniform functional design. These classes are supposed to be composed of individuals of the same age, sex, and species. The correct reference classes to use are supposed to be fixed by nature, with no allowance for physicians to choose between different candidate reference classes, using factors other than age, sex, race, and species. The ability to choose between different candidate reference classes amounts to the ability to choose between different candidate concepts of disease, which Boorse (2014) denies is possible.

I have defended the reference-class problem from several attempts to dismiss it. If the BST is not value-laden, as Boorse (2014) and Werkhoven (2020) claim, then neither are many possible alternative theories of health and disease. The BST fails to show that it, and it alone, is the objective and naturalistic theory. Kingma has not confused the justification of the BST with the meaning of the terms used in it, as Werkhoven (2020) argues. Rather, Kingma (2007) argues that using the BST results in a circular argument, as the assertion of what should count as a reference class is also an assertion about what counts as healthy. Kingma’s argument does not rely on the assertion that disease concepts are value-laden, as Boorse (2014) and Werkhoven (2020) maintain. Rather, Kingma only concludes that the BST is value-laden because Boorse fails to show how it is objective. Werkhoven’s (2020) argument that our intuitions guide us to distinguish healthy conditions from pathological ones is a perfect restatement of Kingma’s concerns. The reference-class problem is a pressing theoretical issue, the practical importance of which is demonstrated by empirical work.

This empirical work has shown that many different reference classes have been and are being used to diagnose low bone mineral density. Age- and sex-adjusted reference classes, or Z-scores, are used to diagnose low bone mineral density in children. Researchers argue that an age-adjusted reference class should be used because children are both growing and function differently from adults. The intuition that the differences in functioning that occur as part of natural development through life stages should be taken into account is present in this literature, which supports the BST. However, physicians do not necessarily use reference classes adjusted for chronological age. They adjust for pubertal age, bone age, height age, and muscle mass. This shows that even if physicians are interested in finding the appropriate natural class of organisms to use as a reference class, there are more factors to consider than age, sex, race, and species.

Furthermore, physicians argue that these additional factors should be used to define reference classes because they are correlated with bone mineral density in healthy patients. When bone mineral density of healthy patients is assessed against these additional factors, the differences in functioning among healthy patients largely disappear, making researchers want to control for these healthy differences in functioning. The process of calibrating their reference classes involves prior knowledge of which patients are healthy. This is one of the main concerns raised by the reference-class problem. These reference classes are not just age adjusted, they are health adjusted. Adjusting reference classes according to health status is incompatible with the BST. This finding lends empirical support for the philosophical concerns raised by critics of the BST, who worry about defining reference classes according to prior knowledge of health.

Looking at how osteoporosis is defined in children has also revealed the role that risk of fracture plays in calibrating reference classes. For many physicians, the choice of reference class is ultimately determined by whether it can be used to predict which patients will sustain fragility fractures, and not by whether it reflects the correct natural class of organisms. Physicians have suggested using different reference classes to achieve different clinical goals. The concepts of disease used in this literature are much more pragmatic than naturalistic.